{
  "abstract": "For a $k$-uniform hypergraph $\\mathcal H$, the shadow of $\\mathcal H$ is the graph whose edges are the pairs covered by a hyperedge. In this paper, for all sufficiently large $n$, we determine the $n$-vertex $k$-uniform hypergraphs of maximum adjacency-tensor spectral radius whose shadow has no $K_t$ minor, for every $t\\ge k+1$, and those whose shadow has no $K_{s,t}$ minor, for every $2\\le s\\le t$ with $s+t\\ge k+1$ and every residue of $n-s+1$ modulo $t$; outside these ranges the problems are trivial. This extends to uniform hypergraphs the theorem of Tait on graphs with no $K_r$ or $K_{s,t}$ minor, whose remaining residues were settled by Zhai and Lin. In each case the extremal hypergraph is unique, and it is the $k$-clique hypergraph of the join of a clique with a graph that we call the light part. For $K_{s,t}$ the answer depends on $j=k-s+1$. When $j\\le1$, the maximum has order $n^{(k-1)/k}$, and the light part is the one found by Zhai and Lin for the adjacency matrix, including its exceptional components. When $j\\ge2$, a regime that does not occur for graphs, the maximum has order $n^{(s-1)/k}$ and $t$ enters its leading constant. The light part then consists of copies of $K_t$ and one smaller clique, with a single exception: for $(k,s,t)=(9,8,8)$ and $n-s+1\\equiv2\\pmod 8$, the complement of the Petersen graph appears. When the smaller clique has between $1$ and $j-1$ vertices, the extremal graph is not unique. In particular, for $t=8$, $4\\le s\\le7$, $k=s+1$ and $n-s+1\\equiv2\\pmod 8$, the clique hypergraph of the extremal graph of Zhai and Lin is not extremal. For $j\\ge2$ the light part is determined by a weighted clique inequality, which for $j\\ge3$ follows from a weighted form of the closed-neighborhood counting of Chao and Dong.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22370",
  "author_total": 2,
  "authors": [
    {
      "name": "Pei Liu"
    },
    {
      "name": "Suil O"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bmt3hxp3wrtf5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22370",
  "fulltext_url": null,
  "id": "bmt3hxp3wrtf5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22370",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2608|Graph theory and applications"
    ]
  ],
  "openalex": "W7214031189",
  "pdf_url": "https://arxiv.org/pdf/2609.22370",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bmt3hxp3wrtf5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.22370",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22370"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The maximum spectral radius of uniform hypergraphs whose shadow excludes a complete or complete bipartite minor",
  "title_text": "The maximum spectral radius of uniform hypergraphs whose shadow excludes a complete or complete bipartite minor",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/bmt3hxp3wrtf5",
  "venue": "arXiv",
  "versions": []
}